A 15-cm 3 20-cm integrated circuit board is to be cooled by attaching 4-cmlong
aluminum (k 5 237 W/m∙K) fins on one side of it (Fig. 3–50). Each fin
has a 2-mm 3 2-mm square cross section. The surrounding ambient temperature
is 25°C and the convection heat transfer coefficient on each fin surface is
20 W/m2∙K. To prevent the circuit board from overheating, the upper surface
of the circuit board needs to be at 85°C or cooler. Design a finned surface having
the appropriate number of fins, with an overall effectiveness of 3 that can
keep the circuit board surface from overheating.